Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON3):

Solution:
n = int(input())
top = int(((8*n-7)**.5-1)/2) + 1
flag = False
for m1 in range(1, top):
    m2 = int(((8*n + 2 - (2*m1+1) ** 2) ** .5 - 1)/2)
    if (2*m1 + 1) ** 2 + (2*m2 + 1) ** 2 == 8*n + 2:
        flag = True
        break
if flag:
    print("YES")
else:
    print("NO")